Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.*;;

public class Main {
    
    public void run() {
        List<Integer> L = new ArrayList<Integer>();
        int sum = 0;
        int n = cin.nextInt();
        for (int i = 1; sum <= n; ++i) {
            sum += i;
            L.add(sum);
        }
        for (int i = 0; i < L.size(); ++i) {
            if (Collections.binarySearch(L, n - L.get(i)) >= 0) {
                out.println("YES");
                return;
            }
        }
        out.println("NO");
    }

    public static void main(String[] args) throws IOException {
        Main sloved = new Main();
        sloved.run();
        sloved.out.close();
    }

    Scanner cin = new Scanner(System.in);
    PrintWriter out = new PrintWriter(System.out);
}